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Scalable Voltage-Stability Dataset Generation Via Boundary-Proximity Indicators Clustering
Rock Agon, Robin Preece, Jovica V. Milanović
TL;DR
Voltage-stability-constrained planning needs large CPF-labelled datasets for machine-learning surrogates, but CPF evaluation is computationally costly. The paper combines feasible-space sampling, sensitivity-guided stress, and hierarchical clustering with representative-medoid CPF labelling; on the IEEE 39-bus system, this reduced CPF computations by 22x while retaining high surrogate accuracy and boundary fidelity.
Problem
CPF-based labelling is computationally costly, yet machine-learning surrogates require large labelled datasets for voltage-security outcomes.
Method
The framework combines physics-informed sampling, sensitivity-guided stress augmentation, hierarchical clustering on boundary indicators, and representative-medoid CPF labelling.
Results
22x fewer CPF computations were achieved on the IEEE 39-bus system while reduced-CPF datasets retained high surrogate accuracy and boundary fidelity for regression and classification.
Takeaways & Limitations
The framework supports efficient and interpretable voltage-stability assessment for planning and operation optimizations.
Takeaways & Limitations
The demonstrated framework is scoped to the specific IEEE 39-bus system case and samples operating points from a DC-feasible polytope rather than an AC-feasible set.
Abstract
from arXiv · showhide
This paper proposes a scalable framework for voltage-stability dataset generation. Voltage-stability-constrained planning increasingly relies on machine-learning surrogates but training them requires large datasets labelled by continuation power flow (CPF) results, which is computationally costly. To address this, this paper proposes a framework that uses hierarchical clustering on boundary-proximity indicators to reduce the number of required CPF evaluations. The proposed approach combines (i) uniform sampling of feasible operating space using Hit-and-Run Markov Chain Monte Carlo, (ii) structured stress directions via maximin Latin hypercube sampling (LHS), (iii) sensitivity-guided perturbations to target weak buses, and (iv) clustering-based representative CPF labelling that reconstructs the voltage stability margins of unlabelled operating points from representative cluster medoids. Results on the IEEE 39-bus system show that the proposed framework significantly reduces CPF evaluations by 95.45% while preserving high accuracy and boundary fidelity for both regression and classification tasks. The reduced surrogates remain structurally consistent with their full-CPF dataset counterparts, demonstrating the suitability and scalability of the proposed approach for operation and planning optimization.
1 Introduction
Voltage stability margins are essential for power-system operation and planning, but CPF-based labelling is costly for the large datasets required by machine-learning surrogates. The proposed framework reduces CPF evaluations by clustering operating points with similar boundary-proximity indicators and labelling each cluster through a representative point.
- Motivation: CPF accurately identifies voltage stability margins but is computationally intensive across large scenario sets.The cost is especially problematic when generating large labelled datasets for machine-learning models.
- Motivation: Existing random, guided, sequential, and probabilistic sampling methods still depend heavily on CPF-based labelling.These methods improve feasible-space and near-boundary coverage but retain the dominant labelling cost.
- Proposed framework: The framework groups operating points by lowest bus voltage, smallest reactive-power reserve, and highest voltage sensitivity to reactive disturbances.These indicators characterize how operating points respond to stress near the voltage-stability boundary.
- Proposed framework: Clustering-based labelling runs CPF on representative points, reducing evaluations while preserving voltage-boundary fidelity.Voltage stability margins from representative cluster points are used to label other operating points in the same cluster.
- Proposed framework: The proposed dataset-generation framework combines uniform sampling with sensitivity-based stress toward the stability boundary.Its contributions include clustering-based labelling and surrogate-to-polyhedra conversion for explicit linear inequalities.
2.1 Proposed voltage-stability dataset generation technique
The proposed dataset-generation technique samples feasible operating conditions, augments them with sensitivity-guided stress, and labels them using representative cluster medoids rather than CPF evaluation at every point. It combines feasible-space sampling, targeted boundary coverage, and clustered representative labelling under a critical N–1 contingency.
- Dataset-generation pipeline: The pipeline comprises feasible-space sampling, sensitivity-guided stress augmentation, and voltage-stability labelling under a critical N–1 contingency.Each operating point includes pre-contingency network-state features and a corresponding post-contingency voltage stability margin.
- Operating-point sampling: Samples are drawn from a DC-feasible polytope defined by generator limits, load bounds, power balance, and transmission limits.SVD incorporates the power-balance equality, while the John-ellipsoid algorithm reshapes the region before Hit-and-Run sampling.
- Operating-point sampling: ACOPF converts each DC-feasible sample into the closest AC-feasible operating state, discarding samples that fail AC convergence.The retained AC-feasible points become seeds for sensitivity-guided stress augmentation.
- Sensitivity-guided stress augmentation: Maximin LHS supplies candidate load-stress directions, and the highest-scoring directions are retained after measuring voltage drop per perturbation.Each direction is scored by perturbing seed loads and resolving power flow; retained directions trigger the ACOPF-CPF labelling pipeline.
- Sensitivity-guided stress augmentation: Classification sampling targets the High Information Content zone around the boundary, placing at least 75% of points there.Regression sampling instead covers the full feasible range of voltage stability margins by uniformly sampling stress amplitudes after finding the collapse-driving maximum.
- Representative medoid labelling: CPF is executed for each medoid under the critical contingency, and its post-contingency voltage stability margin is propagated to the other cluster members.Adaptive CPF step sizes and a loading target typically twice the base-case loading level are used.
- Representative medoid labelling: Hierarchical clustering groups standardized boundary-indicator vectors and represents each cluster with a medoid.The indicators are lowest voltage, lowest reactive-power reserve, and highest bus voltage sensitivity to reactive disturbances.
2.2 Existing voltage-stability dataset generation technique
The existing technique independently labels every operating point by applying the critical N–1 contingency and computing its post-contingency VSM with CPF. This accurate approach has a cost that scales linearly with dataset size because CPF dominates the total computation.
- Conventional labelling: Each operating point is independently labelled after applying the critical N–1 contingency and computing post-contingency VSM with CPF.This procedure is the comparative baseline for the proposed representative-medoid labelling strategy.
- Conventional labelling: CPF cost scales linearly with dataset size in the conventional approach.CPF dominates the total computational cost of dataset generation.
2.3 Surrogate learning the voltage-stability rules
The paper trains sparse oblique decision-tree surrogates to model voltage stability margins and classifications while preserving interpretability and compatibility with optimization. Oblique, sparse splits better represent tilted stability boundaries than axis-aligned alternatives.
- Sparse oblique trees model voltage stability margins and secure/insecure classifications using separate regression and classification models.The regressor predicts the voltage stability margin, while the classifier predicts whether it exceeds a predefined threshold.
- SORT partitions operating-state space into polyhedral regions and assigns each region a constant margin estimate.Each internal node uses a sparse linear split of the form w⊤x ≤ t.
- Sparse splits use at most nsparse features, preserving interpretability and the structure required for downstream MILP embedding.Candidate features are ranked by their correlation with the stability margin before fitting the oblique direction.
- SORT selects split directions from regularized regression or logistic separation, then chooses thresholds using variance or entropy-weighted impurity reduction.Regression trees scan projected operating points to reduce margin variance, while classification trees use information gain with a balance penalty.
- Secure root-to-leaf paths become linear inequalities defining convex polyhedra, and the extracted safe region is their union.This transformation produces explicit mathematical rules suitable for optimization and interpretation.
3 Results
The IEEE 39-bus evaluation shows that clustering-based CPF reduction preserves surrogate accuracy, voltage-boundary fidelity, and much of the decision geometry while concentrating errors in non-binding interior regions.
- Clustering quality: ρ = 0.81 makes minimum reactive-power reserve the strongest predictor of normalized CPF-margin distance, followed by minimum voltage (ρ = 0.70) and voltage sensitivity (ρ = 0.53).The combined indicator distance achieves ρ = 0.78, confirming that nearby clustering points tend to have similar stability margins.
- Clustering quality: MAE below 0.002 at K = 1000 is achieved near the stability boundary, while far-from-boundary MAE reaches approximately 0.008.Intermediate-region MAE saturates around 0.004 beyond K = 800; deep-interior points are typically non-binding in optimization.
- Clustering quality: 1,000 clusters preserve strong agreement between propagated and CPF-computed margins, with larger residuals appearing only at high VSM values.K = 1000 was selected because improvements beyond approximately K = 400 were marginal and classification is sensitive near the security threshold.
- Surrogate modelling quality: The reduced-CPF SORT surrogate has MAE 0.0048 versus 0.0036 for full-CPF SORT, while reduced-CPF SWOCT retains 96.77% precision and 92.89% accuracy.These reduced datasets require only 1,000 CPF evaluations during generation.
- Full vs. reduced-CPF surrogates: preservation of the decision geometry: The reduced-CPF and full-CPF regressors assign near-identical leaf margins, with the largest disagreement of 1.2×10^-2 occurring at a deep-interior leaf.This high-margin region does not enter the binding constraint set.
- Full vs. reduced-CPF surrogates: preservation of the decision geometry: The SWOCTs agree on 15/16 leaves, and their root splits emphasize the same reactive-corridor stress through Qf,3→4 and the substituted Qf,10→11.SORT split alignment is strongest at the root and decays with depth, with depth-3 substitutions remaining within the same physical mode.
4. Conclusion
The framework uses representative CPF approximation to generate voltage-stability datasets, reducing CPF computations by 22x on the IEEE 39-bus case while preserving boundary fidelity and surrogate structure.
- 22x fewer CPF computations were achieved on the specific IEEE 39-bus system case while preserving boundary fidelity.The reduction uses representative CPF approximation within the proposed dataset-generation framework.
- Reduced-CPF datasets maintained 92% surrogate accuracy for both regression and classification tasks.
- The reduced datasets showed strong structural consistency with their full-CPF counterparts.
- The framework supports efficient and interpretable voltage-stability assessment for planning and operation optimizations.